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Dynamic Data Analysis – v5.12.01 - © KAPPA 1988-2017
Chapte
r 6 – W ell models -p188/743
There are two additional parameters that needs to be specified in this model; the fracture
width (w) and the fracture permeability (k
f
), in fact it is the permeability thickness of the
fracture that is specified (k
f
w).
When the fracture conductivity is very high, the model approaches the infinite-conductivity
response, with a ½-slope developing immediately. Conversely, with low k
f
w the pressure drop
along the fracture is significant almost to the onset of radial flow (IARF). When such flow
occurs the relationship between the pressure change and the fourth root of elapsed time is
given be the flowing relationship:
4/1
4/1
11.44
t
kc wkh
qB
p
t
f
6.E.3
Loglog Analysis
From the previous section, the pressure change during bi-linear flow is:
4/1
4
11.44
kc wkh
qB
m where
t mp
t
f
p t m
t
m
t
td
pd
t
t
d
pd
p
4
1
4
1
4
)
ln(
4
4
'
On a decimal logarithmic scale this writes:
)4 log(
)
log(
)'
log(
)
log(
4
1
)
log(
)
log(
p
p
and t
m p
During bi-linear flow the pressure change and the Bourdet derivative follows two parallel
straight lines with a slope of one quarter (1/4). The level of the derivative is a quarter of that
of the pressure change.
This is followed by the onset of linear flow and the pressure change and the Bourdet derivative
follow then two parallel straight lines of half slope (1/2) with the level of the derivative half
that of the pressure change.
When radial flow is reached we have the usual stabilization of the derivative curve.